A hybrid Windkessel-Womersley model for blood flow in arteries

Abstract

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations. In addition, we defined a 6-elements Windkessel model (WK6) in which the blood flow in the connecting tube is modeled by the one-dimensional unsteady Bernoulli equation. Both models have been applied and validated using several aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The results have shown that, both models were able to accurately reconstruct arterial input impedance, however, only the WK-W model was able to calculate the radial distribution of the axial velocity in the aorta and consequently the model predicts the time-varying wall shear stress, and frictional pressure drop during the cardiac cycle more accurately. Additionally, the hybrid WK-W model has the capability to predict the pulsed wave velocity, which is also not possible to obtain when using the classical Windkessel models. Moreover, the values of WK-W model parameters have found to fall in the physiologically realistic range of values, therefore it seems that this hybrid model shows a great potential to be used in clinical practice, as well as in the basic cardiovascular mechanics research.

Keywords: Arterial system; Pulsatile blood flow; Windkessel model; Womersley solution.